
as \(k\rightarrow \infty \) , after another subsequence extraction. Recalling the growth assumptions on \(G\)  and \(G^{\prime }\)  imposed in (REF ), we use the above convergences along with Lebesgue's general convergence theorem (see [1]}) to deduce that
\(G(\alpha \Psi _k) &\rightarrow G(\alpha \Psi )&&\quad \text{strongly in $L^1(\Sigma )$, and a.e.~on $\Sigma $,}\\G^{\prime }(\alpha \Psi _k) &\rightarrow G^{\prime }(\alpha \Psi )&&\quad \text{strongly in $L^2(\Sigma )$, and a.e.~on $\Sigma $,}\) 
